CN115407197B - Motor fault diagnosis method based on multi-head sparse self-encoder and Goertzel analysis - Google Patents

Abstract

The present invention discloses a motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis, detects the vibration signal caused by the motor position sensor fault, and obtains the vibration signal spectrum of the corresponding fault; uses the Goertzel algorithm as a narrowband harmonic analysis tool for the fault spectrum, evaluates the second harmonic component of the vibration signal spectrum caused by the motor position sensor fault, and uses it as the excitation feature of the fault detection, and then uses the fourth harmonic component of the vibration signal to complete the extraction of the misalignment fault or breakdown fault feature of the motor position sensor; proposes a multi-head sparse autoencoder deep neural network to jointly learn the motor fault features, thereby realizing unsupervised reconstruction and supervised classification of motor fault data. The present invention does not need to perform the pre-training and fine-tuning required by the classic DNN. By directly training the MH-DNN with a linear unit activation function with a correction function, the computational burden can be reduced, the fault diagnosis performance is good, and the prediction accuracy is improved.

Description

Motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis

Technical Field

The present invention relates to the technical field of motor fault diagnosis, and in particular to a motor fault diagnosis method based on a multi-head sparse autoencoder and Goertzel analysis.

Background Art

With the advancement of modern science and technology, the development of production systems and the improvement of equipment manufacturing level, the number of motors used in production systems is increasing. The normal operation of motors is of great significance to ensure the safe, efficient, high-quality and low-consumption operation of the production and manufacturing process. Motor fault diagnosis technology has emerged in this context. Motor fault diagnosis technology includes multiple technical disciplines. It can judge whether the motor is running normally based on various information generated during the operation of the motor. The fault location and cause can be found without disassembly. Therefore, motor fault prediction and health management are of great significance to industrial development. Common brushless DC motor drivers cause faults such as misalignment due to position sensors. Due to manufacturing defects, the position sensor can be installed in the leading or lagging position, resulting in negative or positive commutation angle errors, respectively. In the case of position sensor misalignment, it will affect the motor rotor position feedback, resulting in alternating faults and generating additional vibration signals. These oscillations will cause the motor current to increase, which will lead to motor current fluctuations and mechanical oscillations. The motor current and torque will be affected, reducing system performance and threatening the expected life of the motor. This will threaten the normal operation of the motor controller circuit and motor windings and affect the performance of the drive system.

Summary of the invention

Purpose of the invention: In view of the misalignment fault and breakdown fault of the brushless DC motor drive caused by the position sensor, the present invention provides a motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis, and utilizes piezoelectric sensors, Goertzel harmonic analysis and multi-head sparse autoencoder classification methods to make the test classification system more flexible and non-invasive, reduce the computational burden, and be more suitable for fault diagnosis caused by position sensors.

Technical solution: The present invention discloses a motor fault diagnosis method based on a multi-head sparse autoencoder and Goertzel analysis, comprising the following steps:

Step 1: Detect the vibration signal caused by the motor position sensor fault through the piezoelectric sensor, complete the front-end signal acquisition of the breakdown fault or dislocation fault signal of the position sensor, and obtain the vibration signal spectrum of the corresponding fault;

Step 2: Use the Goertzel algorithm as a narrowband harmonic analysis tool for the fault spectrum to evaluate the second harmonic component of the vibration signal spectrum caused by the motor position sensor fault and use it as the excitation feature for fault detection. Then use the fourth harmonic component of the vibration signal to extract the misalignment fault or breakdown fault feature of the motor position sensor.

Step 3: A multi-head sparse autoencoder deep neural network (MH-DNN) is proposed to jointly learn motor fault features to achieve unsupervised reconstruction and supervised classification of motor fault data; the multi-head sparse autoencoder deep neural network (MH-DNN) constructs a multi-hidden layer encoder and a decoder, the structure and the number and size of hidden layers of the decoder and the encoder are completely symmetrical, and a classification module is added on the basis of traditional SAE; the encoder uses multi-layer nonlinear transformation to extract high-level representation features from the input data, which are used as inputs of the decoder and the classification module, the decoder reconstructs the input data, and the classification module predicts the input data; the MH-DNN uses a cost function to complete training, directly trains a linear unit activation function with a correction function, and completes the classification of the health status and fault types of healthy and faulty motors.

Furthermore, the step 1 specifically includes the following steps:

Step 1.1: Construct a fault signal acquisition system, using a three-phase voltage source inverter (VSI) to drive a brushless DC motor. The test circuit includes a set of seven 5kHz active first-order low-pass filters, two integrated operational amplifiers, and a piezoelectric ceramic sensor installed on the experimental device. The analog channel is sampled and digitized at 10kHz and 12-bit accuracy, and data is stored and processed;

Step 1.2: Establish a brushless DC motor model with a built-in Hall effect position sensor, obtain the change rules of the motor back EMF and rotor position phase current waveform when the position sensor fails, and complete the configuration of the brushless DC motor drive controller;

Step 1.3: Establish a piezoelectric sensor model and its electrical simulator. By monitoring the vibration signal of the piezoelectric sensor, the torque and speed oscillation signals caused by faults such as position sensor misalignment can be obtained.

Furthermore, the specific operations of step 1.2 are as follows:

(1) Obtaining the state space of the brushless DC motor control circuit

For a brushless DC motor with a neutral point, the state space of its control circuit is:

Among them, V _xs , R, L _s , M, i _x (x=a,b,c), _exs , _Ke , f(θ) represents phase voltage, phase resistance, self-inductance, mutual inductance, phase current, back-EMF, back-EMF constant, mechanical rotor angular velocity and trapezoidal function respectively;

(2) Establishing the mechanical dynamics model of the brushless DC motor drive control system

The electromagnetic wave torque generated by the mechanical dynamics model of the brushless DC motor drive control system is shown in the following formula:

Among them, θ _m , _TL , B, and J are the rotor position, load torque, friction torque coefficient, and mechanical inertia, respectively;

(3) Based on the output of the position sensor and the required direction of rotation, the waveforms of the motor back EMF and rotor position phase current are obtained, and the controller configuration data for the six sectors of the electrical cycle are determined.

Furthermore, the specific operations of step 1.3 are:

(1) Establishing a piezoelectric sensor model

The piezoelectric sensor is mounted on a circular brass plate (negative electrode) and coated with a thin metal film as the positive electrode. The piezoelectric sensor model is established, and its forward and reverse piezoelectric effects are:

Where D _i is the electric displacement component, d _ikl and d _kij are the piezoelectric coefficients, T _kl is the pulling vector component, is the dielectric constant component under constant conditions, E _k is the electric field component, S _ij is the strain component, s _ijkl ^E is the flexibility constant under constant electric field, i, j, k, l represent the natural coordinates of the piezoelectric crystal system, and the values are 1, 2 and 3;

(2) Establish an electrical simulator using the Butterworth-Van Dyke (BVD) model;

(3) Use piezoelectric sensors to detect vibration signals caused by position sensor failure.

Furthermore, the implementation process of the Goertzel algorithm in step 2 is as follows:

Step 2.1: First, calculate the components of the kth discrete Fourier transform (DFT) of the signal x[n]:

Among them, the feature length is N, k is an integer;

Step 2.2: Find the first-order difference equation for the expected value of y _k [n]:

Step 2.3: Solve the second-order difference equation:

Step 2.4: Obtain the final expression based on Goertzel harmonic analysis:

Furthermore, the specific steps of constructing a multi-hidden layer encoder in step 3 are as follows:

1) First, a single-layer encoder is constructed, from the input layer to the hidden layer, called an encoder. The single-layer encoder receives a sample x as input and converts the input D-dimensional sample x into its hidden layer output, expressed as a = [a ₁ , a ₂ , a ₃ , … a _D1 ], a = σ(W ₁ x+b ₁ ), where σ is the activation function, W ₁ , b ₁ are the weight matrix and bias vector of the encoder;

2) Based on the single-layer encoder, a multi-hidden layer encoder is constructed; L hidden layers are used to extract high-level features of the encoder, where L∈N, let a ₁ ,a ₂ ,…,a _L be the features extracted from the corresponding hidden layer, and its dimension is D ₁ ,D ₂ ,…,D _L ;

3) Dimension setting: _D1 is set to a value greater than the input layer D to obtain the sparse over-complete representation features of the first hidden layer; the dimension of the remaining hidden layer is _Dl , l = 2, 3, ..., L, which is less than _Dl-1 to obtain compressed features;

4) The ReLU activation function is used for the input layer and all hidden layers. In all hidden layers, sparse regularization is applied to extract discriminative features, and L2 regularization is used to constrain the weights of the encoder:

Among them, R _sp is sparse regularization, which is calculated using the Kullback-Leibler (KL) divergence function to measure The closeness to the expected sparse ratio p is When it is equal to p, the KL function is zero; is the average activation of the jth hidden neuron, considering all input samples x _i , i = 1,…,N, which is defined as follows: a _i,j is the jth element of the i-th hidden feature.

Furthermore, the specific steps of constructing the decoder in step 3 are:

1) The decoder is from the hidden layer to the output layer, and reconstructs the input sample x according to the feature vector a The structure, number and size of hidden layers of the decoder and encoder are completely symmetrical. The decoder uses the feature a _L to recover the input data x as follows:

Among them, W ₂ , b ₂ are the weight matrix and bias vector of the decoder respectively;

2) All hidden layers use ReLU activation function, all output layers use sigmoid activation function, and L2 regularization is used to constrain the weights of the decoder;

3) Add sparse restrictions during network training, and the sparse encoder completes the extraction of discriminative features:

Assume that the input sample is x _i , i = 1,…,N, and the training objective is to minimize the following cost function:

Among them, the first term is the reconstruction error, the second term is the _L2 regularization term, W is the SAE weight matrix, _Rsp is the sparse regularization, λ and β are the weight control parameters of the corresponding terms, _Rsp is the sparse regularization, calculated using the Kullback-Leibler (KL) divergence function to measure The closeness to the expected sparse ratio p is When p is equal to p, the KL function is zero:

in, is the average activation of the jth hidden neuron, considering all input samples x _i , i = 1,…,N, which is defined as follows: a _i,j is the jth element of the i-th hidden feature.

Furthermore, the specific steps of constructing the classification module in step 3 are:

1) MH-DNN adds a classification module based on the traditional SAE. The classification module uses a softmax layer with C neurons. The output of the neural network is converted into a probability expression through the softmax layer, thereby finding the maximum probability item and classifying it; the softmax layer represents different conditions for solving C-class classification problems. When the feature a _L is given, the softmax layer calculates the output vector y ₁ ,y ₂ ,…,y _C , where the kth output is y _k , k＝1,2,…,C, and its specific definition is as follows:

Among them, 0≤y _k ≤1, Z _k is the k-th output before applying the softmax activation function. Dropout regularization is used on the hidden layer of the classification module. Z _k is calculated using the following equation:

z _k = w _k (a _L or) + b _k

Where _wk and _bk are the weight and bias of the kth neuron in the softmax layer, o is the element-wise multiplication operator in vector multiplication, _aL is the given feature, is the "masking" vector of Bernoulli random variables, whose probability is 0;

2) Assume that the data in the training set is represented as ( _xi , _yi ), i = 1, 2, ..., N, and each label _yi is transformed into a C-dimensional vector, that is, (yi _,1 , yi _,2 , ... yi _,c ) _{i = 1, 2, ..., N} :

3) Use the cost function to complete the training

The training objective of the multi-head sparse autoencoder deep neural network (MH-DNN) is to minimize the following cost function:

Among them, the first term is the reconstruction error, the second term is the L2 regularization term, yi _,k is the C-dimensional vector converted from _yi , _xi is the input sample, is the decoder output, N is the data length, W is the weight matrix of the entire MH-DNN, is the sparse regularization applied to the jth hidden layer of the encoder, the last term is the cross entropy loss parameter of the classification module, and λ, β, η ₁ , η ₂ are the weight control coefficients of the related terms.

Beneficial effects:

1. The present invention uses piezoelectric sensors, Goertzel analysis and multi-head sparse autoencoder classification to complete the process of motor fault diagnosis, and correctly predicts the misalignment fault and breakdown fault caused by the position sensor. In the motor fault signal acquisition, a piezoelectric sensor is used to collect the vibration signal caused by the position sensor failure. Piezoelectric sensor is an inexpensive testing technology with flexibility and non-invasiveness. This method can be used as an external diagnostic tool to detect all potential Hall effect-based position sensor fault types, such as misalignment or single breakdown fault or double breakdown fault, without the need to modify the motor hardware, change the controller or add external voltage or current sensors. Therefore, this method is independent of the voltage and current of the drive system and the position sensor, which can minimize the system connection lines and eliminate the need for motor-based position sensor mapping. There is no need to double the position sensor or add logic circuits, which can achieve local or remote monitoring of the motor health or fault status.

2. The present invention uses the Goertzel algorithm to perform harmonic analysis of fault vibration signals. The Goertzel algorithm can be used for frequency domain analysis by using only a narrow frequency band around the harmonic component of interest, which is relatively advantageous. The Goertzel algorithm does not require normalization, and there are no other high-amplitude harmonic components within the studied spectrum, so the scope can be further narrowed, and the implementation process is faster, which is suitable for applications such as motor fault diagnosis and condition monitoring.

3. The present invention proposes a multi-head sparse autoencoder deep neural network (MH-DNN) to jointly learn motor fault characteristics, thereby completing the classification of the health status and fault type of healthy and faulty motors for testing. The focus is on constructing a multi-hidden layer encoder and a decoder with a completely symmetrical number and size of hidden layers, and adding a classification module. This method does not require the pre-training and fine-tuning stages required by the classic DNN, and directly trains a linear unit activation function with a correction function, which can reduce the computational burden, is beneficial to improving the reliability of motor production, and reducing maintenance costs, and has great practical significance for motor detection and maintenance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a brushless DC motor fault signal acquisition system based on a position sensor;

FIG2 is a dimensional diagram of a brushless DC motor;

Figure 3 is a diagram of the motor winding leads;

FIG4 is a block diagram of a typical brushless DC motor driver with a built-in Hall position sensor;

FIG5 is the waveform of the ideal motor back EMF (Ex) and rotor position phase current (Ix) (x = A, B, C);

FIG6 is a simplified block diagram of the forward and reverse piezoelectric effects based on different mechanical and electrical properties;

FIG7 is the Butterworth-Van Dyke (BVD) model of a piezoelectric sensor;

FIG8 is a block diagram of an implementation of a second-order Goertzel algorithm;

FIG9 is a flow chart of motor fault frequency analysis and feature extraction based on the Goertzel algorithm;

FIG10 is a narrow spectrum of a piezoelectric sensor based on Goertzel analysis;

FIG11 is a phase current waveform when the position sensor fails (high position configuration);

FIG12 is a phase current waveform when the position sensor fails (low position configuration);

FIG13 is the structure of a single-layer sparse autoencoder (SAE);

Figure 14 is a multi-head sparse autoencoder deep neural network (MH-DNN) structure;

Figure 15 is the process of the motor fault diagnosis method based on the multi-head sparse autoencoder deep neural network (MH-DNN).

DETAILED DESCRIPTION

The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are provided to explain the present invention, but the present invention is not limited to the following embodiments.

Aiming at the misalignment fault and breakdown fault of the brushless DC motor driver caused by the position sensor, the present invention provides a motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis. This method using piezoelectric sensor, Goertzel harmonic analysis and multi-head sparse autoencoder classification makes the test classification system more flexible and non-invasive, reduces the computational burden, and is more suitable for fault diagnosis caused by position sensor.

FIG1 shows a brushless DC motor fault signal acquisition system based on a position sensor in an embodiment of the present invention:

The motor fault signal acquisition system consists of a motor, a piezoelectric ceramic sensor, an integrated operational amplifier, a three-phase voltage source inverter (VSI), a 12-bit precision ADC collector and a computer. The experiment was carried out under the stable operation of the motor without load, mainly collecting the vibration signals of the motor in normal state and fault state. Finally, the collected signals were sent to the computer for fault diagnosis and processing.

In conjunction with FIG1 , the present invention discloses a motor fault diagnosis method based on a multi-head sparse autoencoder and Goertzel harmonic analysis, comprising the following steps:

Step 1: When the motor is running stably without load, use the piezoelectric ceramic sensor to collect the vibration signals of the motor in normal state and the position sensor in fault state;

(1) Build a fault signal acquisition system

The 57BL115S18 brushless DC motor BLDC (180W/3000RPM/DC 24V) was used as the research object, and the motor rotor speed was set to 900rpm, the base frequency was 60Hz, and the motor was unloaded. The brushless DC motor was driven by a three-phase voltage source inverter (VSI). The test circuit included a set of 7 5kHz active first-order low-pass filters, two single-power, low-cost, noise and bias universal integrated operational amplifiers, and the piezoelectric ceramic sensor was installed on the experimental device. The analog channel was sampled and digitized at 10kHz and 12-bit accuracy, and sent to the computer for data storage and processing.

In the specific implementation, the motor size parameters and motor winding lead diagram are shown in Figure 2 and Figure 3. The brushless DC motor parameters are shown in Table 1:

Table 1 BLDC brushless DC motor parameters

(2) Study the brushless DC motor model with built-in Hall effect position sensor, obtain the changing law of the motor back EMF and the waveform of the rotor position phase current, and complete the configuration of the brushless DC motor drive controller;

1) Obtain the state space of the brushless DC motor control circuit

For a brushless DC motor with a neutral point, the state space of its control circuit is expressed by equations (1) and (2):

Among them, V _xs , R, L _s , M, i _x (x=a,b,c), _exs , _Ke , f(θ) represents phase voltage, phase resistance, self-inductance, mutual inductance, phase current, back-EMF, back-EMF constant, mechanical rotor angular velocity and trapezoidal function respectively.

2) Establish the mechanical dynamics model of the brushless DC motor drive control system

The mechanical dynamics model of the brushless DC motor drive control system and the electromagnetic wave torque generated are shown in equations (3) and (4):

Among them, θ _m , _TL , B, J are rotor position, load torque, friction torque coefficient and mechanical inertia respectively, and other parameters are the same as above.

3) Based on the output of the position sensor and the direction of required rotation, the waveforms of the motor back EMF and rotor position phase current are obtained, and based on these waveforms, the controller configuration data for the six sectors of the electrical cycle are determined.

Brushless DC motors usually use built-in Hall effect position sensors, which are a low-cost, small-volume rotor position detection method with 60-degree resolution and speed estimation. The speed update rate is low at low speeds. To be precise, the digital output of each sensor is up to 180 degrees, and the rest of the time is low electrical cycles. The most common configuration is located 120 degrees apart, dividing the electrical cycle into six sectors. Since the typical brushless DC motor drive system has a voltage source inverter, the phase current can be detected and transformed according to the motor rotor position.

A typical block diagram of a brushless DC motor driver with built-in Hall position sensor is shown in Figure 4.

During operation, the power switches are activated according to a predefined sequence to implement the standard 120-degree commutation logic, and there are two active phases in each sector, so each stage includes 120 degrees of positive power on, 60 degrees of power off, 120 degrees of negative power on, and the rest is a stop working state.

The ideal motor back EMF and rotor position phase current waveforms are shown in Figure 5.

It is worth noting that the waveforms in FIG5 are based on the following assumptions: the turn-on and turn-off times of the power switch are ignored, and the corresponding waveforms are obtained when the brushless DC motor (BLDC) has an ideal trapezoidal back EMF and low phase inductance.

The controller configuration to obtain six sectors in one electrical cycle is shown in Table 2.

Table 2 120° commutation logic based on rotor position and sensor signal

In practical applications, the phase currents have a quasi-rectangular waveform, but in most cases they are not completely synchronized with the back EMF, thus affecting the observed current waveform. Torque ripple may occur in normal operation, taking into account the motor inductance and the unavoidable detection processing errors of the rotor position estimation.

(3) A piezoelectric sensor model and its electrical simulator are established. The piezoelectric sensor monitors the vibration signal to obtain the torque and speed oscillation signals caused by faults such as position sensor misalignment. The performance of piezoelectric ceramic sensors in detecting different fault types in brushless DC motor drive systems is studied.

1) Establish a piezoelectric sensor model

According to the direct piezoelectric effect, in some cases, a crystal subjected to external stress will generate surface charges, which will produce polarization, which can be expressed as a voltage difference between the crystal terminals. When these dielectric materials are deformed, they will also exhibit the inverse piezoelectric effect, with the forward and reverse piezoelectric effects expressed by equations (5) and (6), respectively. Here, the output voltage polarity is defined by the orientation of the crystal relative to the pressure.

The specific piezoelectric effect is shown in Figure 6.

S _ij ＝s _ijkl ^E T _kl +d _kij E _k (6)

Where D _i is the electric displacement component, d _ikl and d _kij are the piezoelectric coefficients, T _kl is the pulling vector component, is the dielectric constant component under constant conditions, E _k is the electric field component, S _ij is the strain component, s _ijkl ^E is the flexibility constant under constant electric field, i, j, k, l represent the natural coordinates of the piezoelectric crystal system, and the values are 1, 2 and 3.

2) Build an electrical simulator

The electrical simulator uses the Butterworth-Van Dyke (BVD) model, as shown in Figure 7.

Here, the electronic component _Cm is related to the mechanical elasticity of the electrode, _Lm is the inertial component of the vibrating material, _Rm is the mechanical energy loss caused by the oscillation, and _Co represents the capacitance of the piezoelectric material.

3) Study the application theory and basis of piezoelectric sensors in motor position sensor fault detection, and use zirconate titanium ceramic piezoelectric sensors to detect vibration signals caused by position sensor faults. After preprocessing, the signals are transmitted wirelessly to the computer control system via Wi-Fi.

In the implementation, a zirconate titanium ceramic piezoelectric sensor is used, where the piezoelectric element is mounted on a circular brass plate (negative electrode) and coated with a thin metal film as the positive electrode. The sensor has a small frequency difference and low manufacturing cost.

Due to manufacturing defects, the position sensor can be installed in the leading or lagging position, resulting in negative or positive commutation angle errors, respectively. In the case of misalignment of the position sensor, the motor current and torque will be affected, generating additional vibration signals. Therefore, piezoelectric sensors can be used to diagnose non-ideal installation angles with different or uniform movement. In this patent, piezoelectric sensors are applied to diagnose misalignment faults of position sensors, and the Goertzel algorithm is used to extract fault features from the second harmonic component of the vibration signal.

In this implementation, a single position sensor failure is studied.

As previously mentioned, a position sensor fault can be identified by a permanent output signal of the faulty sensor at a high or low level, regardless of the rotor position. This fault condition affects the phase current commutation because it causes an extended 120 degree sector. For the active phase, in the case of a single sensor breakdown fault, "inhibit" vectors of (0,0,0) and (1,1,1) are also observed. In the present invention, the controller is programmed to react to the inhibit vector by sending a zero vector command at the PWM output terminal to drive the motor windings to a three-phase floating state.

The motor health status and fault status caused by improper sensor position are shown in Table 3:

Table 3 Commutation sequence of motor health status and fault status caused by improper sensor position

Faulty sensors affect phase current commutation in different ways. In the case of defective position sensors, the following conclusions are drawn from the comparison of phase current waveforms:

A single-position sensor breakdown fault imposes an additional zero-current sector or an extended conduction cycle, which may cause a controller power switch failure or an increase in motor winding temperature. In addition, when the back-EMF amplitude decreases from a flat-top value to a lower value, the phase current will increase due to the input voltage and its voltage difference. Therefore, due to the two-phase conduction mode, the other activated phase is also affected, and the current values of both phases are expected to increase. In the case of different position sensor breakdown faults, similar waveforms provide a basis for its fault state prediction.

Step 2: It is proposed to use the Goertzel algorithm as a narrowband harmonic analysis tool for the fault spectrum to evaluate the second harmonic and fourth harmonic components of the vibration signal spectrum caused by the motor position sensor fault, and use it to extract the misalignment fault or breakdown fault characteristics of the position sensor.

In the frequency domain analysis of fault diagnosis, the fast Fourier transform (FFT) is often used. However, its main disadvantages are that its performance such as frequency resolution, spectrum leakage and computational cost are limited. Therefore, the present invention adopts the Goertzel algorithm. The Goertzel algorithm can be used for frequency domain analysis by using only a narrow frequency band around the harmonic component of interest, which has a relatively large advantage. FFT analysis requires the entire spectrum to complete the frequency analysis. Moreover, the Goertzel algorithm does not need normalization. There are no other high-amplitude harmonic components within the studied spectrum range, so the range can be further narrowed and the implementation process is faster. In general, the Goertzel algorithm is superior to FFT in terms of signal length and low memory requirements. Its computational complexity is independent of the signal length and is suitable for applications such as motor fault diagnosis and condition monitoring.

Specifically, the implementation process of the Goertzel algorithm is as follows:

(1) First, calculate the kth discrete Fourier transform (DFT) component of the signal x[n], whose characteristic length is N, as shown in equation (7). Where k is an integer, and the algorithm uses the phase factor e ^j2πk to complete the calculation. Based on the periodicity of e ^j2πk , the computational complexity of the algorithm will be greatly reduced;

(2) Then, the first-order difference equation for the expected value of y _k [n] is obtained, see equation (8), which contains complex numbers and computationally intensive multiplication factors;

(3) Next, the second-order difference equation is obtained, which is specifically expressed by equation (9);

(4) Finally, the expression of the final system is obtained, as described in equation (10);

The flowchart of the second-order Goertzel algorithm used is shown in FIG8 .

In the specific implementation of the motor fault signal feature extraction and analysis using the Goertzel algorithm, when the second harmonic component is detected, the fault diagnosis process will be triggered. Specifically, the motor fault vibration data is first obtained, and then the frequency analysis based on the Goertzel algorithm is performed to determine whether there is a second harmonic component. If not, the frequency analysis is performed again. If the second harmonic component is detected, the fourth harmonic component is detected, and then it is determined whether it is a high-increment fourth fault harmonic component, so as to obtain two sets of feature data, and finally the feature value is sent to the classifier to obtain the final classification result.

The process of motor fault frequency analysis and feature extraction based on Goertzel algorithm is shown in Figure 9.

In the implementation, the Goertzel algorithm is used to analyze the motor fault caused by the position sensor. The system frequency is 60 Hz fundamental frequency and the rated torque is 65%. In the case of a single position sensor misalignment fault, the second harmonic component of the piezoelectric sensor spectrum is analyzed by the Goertzel algorithm. The characteristic output of the corresponding narrow spectrum is shown in Figure 9.

Furthermore, in order to study the breakdown failure of a single position sensor, the fault conditions of the Hall effect position sensor in the high position and low position states are compared. When the Hall effect position sensor continuously outputs a high or low signal, it is identified as a fault signal. The phase current waveforms obtained in the high and low position sensor configurations when faulty are shown in Figures 10 and 11.

Step 3: A multi-head sparse autoencoder deep neural network (MH-DNN) is proposed to jointly learn motor fault features to complete the detection and diagnosis of motor faults, thereby realizing unsupervised reconstruction and supervised classification of motor fault data. The main features are the construction of a multi-hidden layer sparse encoder, a decoder with a completely symmetrical number and size of hidden layers, and the addition of a classification module. Among them, the encoder uses multiple layers of nonlinear transformations to extract high-level representation features from the input data. These extracted features are used as inputs to the decoder and classification module. The decoder aims to reconstruct the input data, while the classification module is used to predict the input data. The specific steps are as follows:

(1) Constructing a multi-hidden layer encoder

First, a single-layer encoder is constructed, from the input layer to the hidden layer, called an encoder. The single-layer encoder receives a sample x as input and converts the input D-dimensional sample x into its hidden layer output, expressed as a = [a ₁ , a ₂ , a ₃ , … a _D1 ], and the specific expression is as follows:

a＝σ(W ₁ x+b ₁ ) (11)

Where σ is the activation function, W ₁ , b ₁ are the weight matrix and bias vector of the encoder.

The structure of a single-layer sparse autoencoder (SAE) is shown in Figure 12.

Next, based on the single-layer encoder, a multi-hidden layer encoder is constructed. L hidden layers are used to extract high-level features of the encoder, where L∈N, and a ₁ , a ₂ , …, a _L are the features extracted from the corresponding hidden layers, and their dimensions are D ₁ , D ₂ , …, D _L .

The setting of dimension has the following provisions and characteristics: 1) D ₁ is set larger than the value of input layer D to obtain sparse over-complete representation features of the first hidden layer; 2) The dimension of the remaining hidden layer D _l , l = 2, 3, ..., L, should be smaller than D _l-1 to obtain compressed features.

In the implementation, the ReLU activation function is used in the input layer and all hidden layers. In all hidden layers, the sparse regularization defined in equation (14) is applied to extract discriminative features, and the L2 regularization is used to constrain the weights of the encoder.

(2) Constructing a decoder

The decoder is from the hidden layer to the output layer, and reconstructs the input sample x according to the feature vector a. The structure, number and size of hidden layers of the decoder and encoder are completely symmetrical. The decoder aims to restore the input data x using the feature a _L. The details are as follows:

Among them, W ₂ , b ₂ are the weight matrix and bias vector of the decoder respectively.

During the reconstruction process, all hidden layers use the ReLU activation function, all output layers use the sigmoid activation function, and L2 regularization is used to constrain the weights of the decoder.

As a variant of the autoencoder, the sparse encoder extracts discriminative features by adding sparse restrictions during network training.

Assume that the input sample is x _i , i = 1,…,N, and the training objective is to minimize the following cost function:

Among them, the first term is the reconstruction error, the second term is the _L2 regularization term, W is the SAE weight matrix, λ and β are the weight control parameters of the corresponding terms, and _Rsp is the sparse regularization, which is calculated using the Kullback-Leibler (KL) divergence function to measure The closeness to the expected sparse ratio p is When it is equal to p, the KL function is zero. The specific definition is as follows:

in, is the average activation of the jth hidden neuron, considering all input samples x _i , i = 1,…,N, which is defined as follows:

a _i,j is the jth element of the i-th hidden feature.

(3) Building a classification module

1) MH-DNN adds a classification module based on the traditional SAE. The classification module uses a softmax layer with C neurons. The output of the neural network is converted into a probability expression through the softmax layer, thereby finding the maximum probability item and classifying it. The softmax layer represents different conditions for solving C-class classification problems. When the feature a _L is given, the softmax layer calculates the output vector y ₁ ,y ₂ ,…,y _C . Among them, the k-th output is y _k , k＝1,2,…,C, and its specific definition is as follows:

In the formula, 0≤y _k ≤1, Z _k is the k-th output before applying the softmax activation function. In order to prevent overfitting, Dropout (random dropout) regularization is used on the hidden layer of the classification module. Therefore, considering Dropout, Z _k is calculated using the following equation, which is defined as follows:

z _k = w _k (a _L or) + b _k (17)

Where _wk and _bk are the weight and bias of the kth neuron in the softmax layer, o is the element-wise multiplication operator in vector multiplication, _aL is the given feature, is a “masked” vector of Bernoulli random variables with probability 0. In practice, gradient computation is done only by backpropagation through unmasked neurons.

2) Convert each label _yi into a C-dimensional vector

Assume that the data in the training set is represented as ( _xi , _yi ), i = 1, 2, ..., N, and transform each label _yi into a C-dimensional vector, that is, (yi _,1 , yi _,2 , ... yi _,c ) _{i = 1, 2, ..., N} , as follows:

3) Use the cost function to complete the training

The training objective of the multi-head sparse autoencoder deep neural network (MH-DNN) is to minimize the following cost function:

Among them, the first term is the reconstruction error, the second term is the L2 regularization term, yi _,k is the C-dimensional vector converted from _yi , _xi is the input sample, is the decoder output, N is the data length, W is the weight matrix of the entire MH-DNN, is the sparse regularization applied to the jth hidden layer of the encoder, the last term is the cross entropy loss parameter of the classification module, and λ, β, η ₁ , η ₂ are the weight control coefficients of the related terms.

The structure of the multi-head sparse autoencoder deep neural network (MH-DNN) is shown in Figure 13.

In the specific implementation of motor fault diagnosis using MH-DNN, first, the original motor fault signal is divided into data samples and a sample library is established. Then, MH-DNN is established and trained using the collected C-class feature data samples of healthy and faulty states. After the model is successfully trained, the test data samples are used to determine whether they belong to the known C class by the MH-DNN classification algorithm, and a fault decision conclusion is given.

The flowchart of the motor fault diagnosis method based on multi-head sparse autoencoder deep neural network (MH-DNN) is shown in Figure 14.

Step 4: Based on the above technologies, build an experimental platform to complete the specific implementation of motor fault classification, mainly completing the following test experiments:

(1) Motor fault diagnosis experiment

The embodiment of the present invention uses a piezoelectric sensor to collect the fault signal spectrum caused by the position sensor, and then uses the Goertzel algorithm as a narrowband harmonic analysis tool to analyze the fault signal spectrum and extract its features. Finally, it is added to a multi-head sparse autoencoder deep neural network (MH-DNN) classifier to obtain the classification results of two types of faults, namely, misalignment fault and breakdown fault.

200 data were collected for different fault and health status signals, and the fault features of the corresponding frequency graph were extracted and sent to the corresponding classifier model to complete the classification of the health status and fault type of healthy and faulty motors. The number of iterations and populations in the algorithm were 1000 and 500 respectively, the threshold and weight values were between [-1,1], and the learning rate was 0.25. The test results are shown in Table 4.

Table 4 Fault diagnosis classification effect

As can be seen from Table 4, the classification accuracy and recall rate of misalignment faults and breakdown faults are similar and perform well. The use of piezoelectric sensors can correctly diagnose the misalignment and breakdown faults of Hall effect position sensors in motor drive control systems. This method is effective for the classification of different faults and has good application prospects. The main advantages of this method are that it can distinguish between the two types of position sensor faults in motor control, use different harmonic components to detect different fault types, and use the Goertzel algorithm of narrowband harmonic analysis, which saves time, computing costs and memory requirements. Therefore, piezoelectric sensors can be used for state monitoring of motor drive systems and are suitable for forming a cheap intelligent Internet of Things for fault diagnosis.

(2) Comparison of different classifier models

In the implementation, the proposed MH-DNN classifier was experimentally verified and compared with the conventional BP algorithm and RBF algorithm. After the model was trained, the error values of the trained network were compared, and 20 groups of samples were randomly selected. The fault samples were sent to the trained model for testing, and the diagnostic results were shown in Table 5.

Table 5 Comparison of experimental results (error)

As can be seen from Table 5, the prediction result based on the multi-head sparse autoencoder deep neural network classifier (MH-DNN) is the best, and its absolute value of prediction error is significantly smaller than that of the BP algorithm and the RBF algorithm. Since the training samples contain motor fault information, compared with the traditional BP neural network and RBF algorithm, the MH-DNN classifier shows obvious advantages in motor fault diagnosis, has a higher diagnostic accuracy, and can obtain a diagnostic effect far higher than that of the BP algorithm and the RBF algorithm.

The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A motor fault diagnosis method based on a multi-head sparse autoencoder and Goertzel analysis, characterized in that it comprises the following steps: Step 1: Detect the vibration signal caused by the motor position sensor fault through the piezoelectric sensor, complete the front-end signal acquisition of the breakdown fault or dislocation fault signal of the position sensor, and obtain the vibration signal spectrum of the corresponding fault; Step 1.1: Construct a fault signal acquisition system, using a three-phase voltage source inverter (VSI) to drive a brushless DC motor. The test circuit includes a set of seven 5kHz active first-order low-pass filters, two integrated operational amplifiers, and a piezoelectric ceramic sensor installed on the experimental device. The analog channel is sampled and digitized at 10kHz and 12-bit accuracy, and data is stored and processed; Step 1.2: Establish a brushless DC motor model with a built-in Hall effect position sensor, obtain the change rules of the motor back EMF and rotor position phase current waveform when the position sensor fails, and complete the configuration of the brushless DC motor drive controller; Step 1.3: Establish a piezoelectric sensor model and its electrical simulator, and obtain the torque and speed oscillation signals caused by the position sensor misalignment fault by monitoring the vibration signal with the piezoelectric sensor; (1) Establishing a piezoelectric sensor model The piezoelectric sensor is mounted on a circular brass plate and coated with a thin metal film as the positive electrode. The piezoelectric sensor model is established, and its forward and reverse piezoelectric effects are: S _ij ＝s _ijkl ^E T _kl +d _kij E _k Where D _i is the electric displacement component, d _ikl and d _kij are the piezoelectric coefficients, T _kl is the pulling vector component, is the dielectric constant component under constant conditions, E _k is the electric field component, S _ij is the strain component, s _ijkl ^E is the flexibility constant under constant electric field, i, j, k, l represent the natural coordinates of the piezoelectric crystal system, and the values are 1, 2 and 3; (2) Establishing an electrical simulator, which uses the Butterworth-Van Dyke (BVD) model; (3) Using piezoelectric sensors to detect vibration signals caused by position sensor failure; Step 2: Use the Goertzel algorithm as a narrowband harmonic analysis tool for the fault spectrum to evaluate the second harmonic component of the vibration signal spectrum caused by the motor position sensor fault and use it as the excitation feature for fault detection. Then use the fourth harmonic component of the vibration signal to extract the misalignment fault or breakdown fault feature of the motor position sensor. Step 3: A multi-head sparse autoencoder deep neural network is proposed to jointly learn motor fault features to achieve unsupervised reconstruction and supervised classification of motor fault data; the multi-head sparse autoencoder deep neural network constructs a multi-hidden layer encoder and a decoder, the structure and the number and size of hidden layers of the decoder and encoder are completely symmetrical, and a classification module is added on the basis of traditional SAE; the encoder uses multi-layer nonlinear transformation to extract high-level representation features from the input data, which are used as inputs of the decoder and classification module, the decoder reconstructs the input data, and the classification module predicts the input data; the multi-head sparse autoencoder deep neural network uses a cost function to complete training, directly trains a linear unit activation function with a correction function, and completes the classification of the health status and fault types of healthy and faulty motors. 2. According to the motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis according to claim 1, it is characterized in that the specific operations of step 1.2 are: (1) Obtaining the state space of the brushless DC motor control circuit For a brushless DC motor with a neutral point, the state space of its control circuit is: Among them, V _xs , R, L _s , M, i _x (x=a,b,c), _exs , _Ke , f(θ) represents phase voltage, phase resistance, self-inductance, mutual inductance, phase current, back-EMF, back-EMF constant, mechanical rotor angular velocity and trapezoidal function respectively; (2) Establishing the mechanical dynamics model of the brushless DC motor drive control system The electromagnetic wave torque generated by the mechanical dynamics model of the brushless DC motor drive control system is shown in the following formula: Among them, θ _m , _TL , B, and J are the rotor position, load torque, friction torque coefficient, and mechanical inertia, respectively; (3) Based on the output of the position sensor and the required direction of rotation, the waveforms of the motor back EMF and rotor position phase current are obtained, and the controller configuration data for the six sectors of the electrical cycle are determined. 3. The motor fault diagnosis method based on the multi-head sparse autoencoder and Goertzel analysis according to claim 1, characterized in that the implementation process of the Goertzel algorithm in step 2 is as follows: Step 2.1: First, calculate the components of the kth discrete Fourier transform (DFT) of the signal x[n]: Among them, the feature length is N, k is an integer; Step 2.2: Find the first-order difference equation for the expected value of y _k [n]: Step 2.3: Solve the second-order difference equation: Step 2.4: Obtain the final expression based on Goertzel harmonic analysis: 4. The motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis according to claim 1 is characterized in that the specific steps of constructing a multi-hidden layer encoder in step 3 are as follows: 1) First, a single-layer encoder is constructed, from the input layer to the hidden layer, called an encoder. The single-layer encoder receives a sample x as input and converts the input D-dimensional sample x into its hidden layer output, expressed as a = [a ₁ , a ₂ , a ₃ , …, a _D1 ], a = σ(W ₁ x+b ₁ ), where σ is the activation function, W ₁ , b ₁ are the weight matrix and bias vector of the encoder; 2) Based on the single-layer encoder, a multi-hidden layer encoder is constructed; L hidden layers are used to extract high-level features of the encoder, where L∈N, let a ₁ ,a ₂ ,…,a _L be the features extracted from the corresponding hidden layer, and its dimension is D ₁ ,D ₂ ,…,D _L ; 3) Dimension setting: _D1 is set to a value greater than the input layer D to obtain the sparse over-complete representation features of the first hidden layer; the dimension of the remaining hidden layer is _Dl , l = 2, 3, ..., L, which is less than _Dl-1 to obtain compressed features; 4) The ReLU activation function is used for the input layer and all hidden layers. In all hidden layers, sparse regularization is applied to extract discriminative features, and L2 regularization is used to constrain the weights of the encoder: Among them, R _sp is sparse regularization, which is calculated using the Kullback-Leibler divergence function to measure The closeness to the expected sparse ratio p is When it is equal to p, the Kullback-Leibler divergence function is zero; is the average activation of the jth hidden neuron, considering all input samples x _i , i = 1,…,N, which is defined as follows: a _i,j is the jth element of the i-th hidden feature. 5. The motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis according to claim 4 is characterized in that the specific steps of constructing the decoder in step 3 are: 1) The decoder is from the hidden layer to the output layer, and reconstructs the input sample x according to the feature vector a The structure, number and size of hidden layers of the decoder and encoder are completely symmetrical. The decoder uses the feature a _L to recover the input data x as follows: Among them, W ₂ and b ₂ are the weight matrix and bias vector of the decoder respectively; 2) All hidden layers use ReLU activation function, all output layers use sigmoid activation function, and L2 regularization is used to constrain the weights of the decoder; 3) Add sparse restrictions during network training, and the sparse encoder completes the extraction of discriminative features: Assume that the input sample is x _i , i = 1,…,N, and the training objective is to minimize the following cost function: Among them, the first term is the reconstruction error, the second term is the _L2 regularization term, W is the SAE weight matrix, λ and β are the weight control parameters of the corresponding terms, and _Rsp is the sparse regularization, which is calculated using the Kullback-Leibler divergence function to measure The closeness to the expected sparse ratio p is When p is equal to p, the Kullback-Leibler divergence function is zero: in, is the average activation of the jth hidden neuron, considering all input samples x _i , i = 1,…,N, which is defined as follows: a _i,j is the jth element of the i-th hidden feature. 6. The motor fault diagnosis method based on multi-head sparse autoencoder and Goertzel analysis according to claim 1, characterized in that the specific steps of constructing the classification module in step 3 are: 1) The multi-head sparse autoencoder deep neural network adds a classification module on the basis of the traditional SAE. The classification module uses a softmax layer with C neurons. The output of the neural network is converted into a probability expression through the softmax layer, thereby finding the maximum probability item and classifying it; the softmax layer represents different conditions for solving C-class classification problems. When the feature a _L is given, the softmax layer calculates the output vector y ₁ ,y ₂ ,…,y _C , where the kth output is y _k , k＝1,2,…,C, and its specific definition is as follows: Among them, 0≤y _k ≤1, Z _k is the k-th output before applying the softmax activation function. Dropout regularization is used on the hidden layer of the classification module. Z _k is calculated using the following equation: z _k = w _k (a _L o r ) + b _k Where _wk and _bk are the weight and bias of the kth neuron in the softmax layer, ο is the element-wise multiplication operator in vector multiplication, _aL is the given feature, is the "masking" vector of Bernoulli random variables, whose probability is 0; 2) Assume that the data in the training set is represented as ( _xi , _yi ), i = 1, 2, ..., N, and each label _yi is transformed into a C-dimensional vector, that is, (yi _,1 , yi _,2 , ... yi _,c ) _{i = 1, 2, ..., N} : 3) Use the cost function to complete the training The training objective of the multi-head sparse autoencoder deep neural network is to minimize the following cost function: Among them, the first term is the reconstruction error, the second term is the L2 regularization term, yi _,k is the C-dimensional vector converted from _yi , _xi is the input sample, is the decoder output, N is the data length, W is the weight matrix of the entire multi-head sparse autoencoder deep neural network, is the sparse regularization applied to the jth hidden layer of the encoder, the last term is the cross entropy loss parameter of the classification module, and λ, β, η ₁ , η ₂ are the weight control coefficients of the related terms.